The formula for calculating the Spearman rank correlation coefficient:
- Spearman’s rank correlation coefficient (ρ):
[
\rho = 1 – \frac{6 \sum d_i^2}{n(n^2 – 1)}
]
where:
- (d_i) is the difference between the ranks for each pair of observations,
- (n) — number of observations.
- Steps for calculation:
Substitute the values into the formula.
Assign ranks to each value in the two data sets.
Calculate the rank difference (d_i) for each pair.
Square each difference (d_i^2).
Find the sum of the squares of the differences (\sum d_i^2).